00:03
All right, 47 here.
00:05
This is a fun little problem.
00:07
We want to use our knowledge of dot product and orthogonal vectors and a little bit of linear algebra.
00:15
And we want to determine what x is, right? so that those vectors are orthogonal.
00:27
So what that means is the dot product is zero, right? the dot product of orthogonal vectors is zero.
00:38
So we simply need to multiply these expressions together that contain x and set it equal to zero.
00:49
Right.
00:49
So what is the dot product? well, that's going to be, oops, didn't switch it to highlighter, sorry.
00:58
Oops, let me fix that.
01:01
Dot product is horizontal components times horizontal components plus vertical components times vertical components.
01:13
Now, if you want to put these in component form first, that'll probably make it a little easier.
01:17
So let's do that.
01:19
So the components of u would be 2x and 3, and the components of v would be x and negative 8.
01:31
All right so if these vectors are orthogonal this dot product is zero so i have a little equation i can solve here right so my dot product means 2x times x plus 3 times negative 8 and that has to equal zero and now we basically just have a quadratic equation to solve here basic one 2x times x is 2x squared.
02:03
3 times negative 8 is going to be minus 24.
02:06
Next, let's add the 24 over.
02:11
And next, we're going to divide both sides by 2.
02:14
So we get x squared equals 12...